(Solved): An airine is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto the ...

An airine is trying two new boarding procedures, Option 1 and Option 2, to load passengers onto their Long Beach (LGB) to San Francisco (SFO) Fights, Since Option 1 has more automation, the airline suspects that the mean Option 1 loading time is less than the mean Option 2 loading time. Fo see if this is true, the airline selects a random sample of 275 flights from LGB to SFO using Option 1 and records their loading times. The sample mean is found to be \( 17.7 \) minutes. with a sample standard deviation of \( 5.5 \) minutes. They also select an independent random sample of 240 flights from L.GB to SFO using Option 2 and record their Ioading times. The sample mean is found to be \( 18.3 \) minutes, with a sample standard deviation of \( 4.5 \) minutes. Since the sample sizes are quite large, it is assumed that the population standard deviation of the loading times using Option 1 and the loading times using Option 2 can be estimated to be the sample standard devation values qiven above. At the \( 0.05 \) level of significance, is there sufficient evidence to support the claim that the mean Option 1 loading time, \( \mu_{1} \) is less than the mean Option 2. loading time, \( \mu_{2} \), for the airline's flights from LGB to SFO? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis \( H_{0} \) and the alternative hypothesis \( H_{1} \). \[ \begin{array}{l} H_{0}: \square \\ H_{1}=\square \end{array} \] (b) Determine the type of test statistic to use,